Contrary to the popular belief that it is the opposite of tsundere, it describes an anime character who is either psychotic or violent or both, and shows affection to the main character. Became a popular moe genre after the airing of the last episode of School Days. Other yandere characters include Ryuuguu Rena from Higurashi No Naku Koro Ni series.

I wish there was a yandere girl who would love me so much she'll want to cleave my head with a hachet.

A common term in otaku fandom, a yandere is a person (usually female) romantically obsessed with someone to the point of using violent means to get them in their arms. Often seen with a sharp weapon and a psychotic grin.

Hey look, Charlotte just killed Karen just for coming within 10 feet of her crush Joey.
Must be a yandere. Avoid at all cost.

Popularized in by the anime/visual novel School Days, yandere is a term for a psychotic girl who's only character traits are being cute or moe and random psychosis. The plot of a yandere story is that the main character falls in love with a girl who isn't the "yandere", where the yandere decides it would be a good idea to kill the love interest, any possible love interest, and finally the main character, because of love. Typically there is no reason for this psychosis because writers are usually lazy.

Rena from Higurashi is not a yandere.
Rena is not a yandere.
RENA IS NOT A YANDERE

Japanese slang for bipolar. A yandere character usually have a lot of mood swings. They have a nice side and an evil side, kinda like ying and yang, white and black... those kind of stuff. They quickly change from the nice side to the evil side, and repeat again and again. It is more often used in anime/manga. There is often another character, usually can be stiff as a board easily, who is normally the 'victim' of the yandere character's evil side.